Question

The sum of the first three numbers in an ap is 18. If the product of the first and the third term is 5 times the common difference, find the numbers.

Answer 1

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Answer 2

Answer:

The terms are either 2,6,10 or 15,6,-3.

Step-by-step explanation:

It is given that the sum of first three numbers in an AP is 18. Product of the first and the third term is 5 times the common difference.

Let first three numbers in the AP are a-d, a, a+d.

Sum of these three terms is 18.

$(a-d)+a+(a+d)=18$

$3a=18$

Divide both sides by 3.

$a=6$

The value of a is 6.

The product of the first and the third term is 5 times the common difference.

$(a-d)(a+d)=5d$

$a^2-d^2=5d$

$6^2-d^2=5d$

$36-d^2=5d$

$d^2+5d-36=0$

$d^2+9d-4d-36=0$

$d(d+9)-4(d+9)=0$

$(d-4)(d+9)=0$

$d=4,-9$

If d=4, then

$a-d=6-4=2$

$a+d=6+4=10$

Therefore the first three terms of the AP are 2, 6 and 10.

If d=-9, then

$a-d=6-(-9)=15$

$a+d=6+(-9)=-3$

Therefore the first three terms of the AP are 15, 6 and -3.